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Acoustic Feedback Part 1 – The Fundamentals

Understanding the fundamental principle behind why a system can oscillate is key to preventing that oscillation.

Anyone who is familiar with the operation of a sound reinforcement system would probably have experienced the dreadful howling sound if the microphone level is set too high.

Before delving into how such acoustic feedback can be avoided, it is essential to understand why acoustic feedback occurs in the first place and what is the associated condition required for such an acoustic feedback.

How Acoustic Feedback Occurs

For a start, consider a very basic sound reinforcement system consisting of a single microphone and a single loudspeaker as shown in Figure 1. Here, the microphone is connected to an audio mixer which then feeds a power amplifier which drives the loudspeaker.

Figure 1: Block diagram of a simple sound reinforcement system

 

In reality, a portion of sound produced by the loudspeaker will find its path to reach the microphone. This can come via off-axis loudspeaker response to microphone or somewhat on-axis loudspeaker response but with the acoustic reflection off walls back to the microphone or a combination of these paths.

For simplicity, consider the case of just a single acoustic feedback path with the attenuation block representing the level of attenuation from the output of the loudspeaker before reaching the microphone as shown in Figure 2. This sound from the loudspeaker sums up with the sound from the sound source at the microphone input.

Figure 2: Block diagram of a simple sound reinforcement system with acoustic feedback path included

 

Suppose that in the beginning, a sound pressure level of 1 unit is being input just for an instant to the microphone. It then goes through amplification at the mixer and power amplifier and finally appears at the loudspeaker.

Suppose that by the time this sound gets back to the microphone, the sound pressure level has half the original level, i.e. 0.5 unit. This 0.5 unit then goes through the same loop and ends up again as half of 0.5 i.e. 0.25 and so on. In brief, we can represent this continuous looping effect by a series of numbers as follows: 1.0, 0.5, 0.25, 0.125, 0.0625, 0.03125, …….

Notice that it started off with 1 unit of sound pressure level and the value decreases over each subsequent loop. For this case, acoustic feedback will not occur since any sound that starts off at the microphone gets attenuated in subsequent loops.

In fact for this case with each loop, half the level of signal is obtained. This is illustrated in Figure 3 where the loop is intentionally open to examine this effect by preventing subsequent looping. When the loop is open, the overall block diagram is characterized by the open loop gain which is 0.5. In decibel, this is equivalent to -6dB by the using 20 log(ratio) formula.

Figure 3: Block diagram of the open loop function, illustrating the open loop gain of 0.5 (-6 dB)

 

If the audio mixer fader is now increased such that the loop gain is increased to 1.0 (i.e. 0 dB), then whatever sound pressure level that is being input to the microphone will end up having the same level after going through the loop. In this case, if the loop is closed, acoustic feedback will occur and the loop gain is just sufficient to be self-sustaining. This case is represented by the series of numbers as follows:
1.0, 1.0, 1.0, 1.0, 1.0, 1.0 …..

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Similarly, if the loop gain is increased to 2.0 (i.e. +6 dB), if the loop is closed, acoustic feedback will definitely occur. The howling will grow louder by an amplitude factor of 2 (i.e. +6 dB) for each loop. This is represented by the series of numbers as follows:
1.0, 2.0, 4.0, 8.0, 16.0, 32.0

The howling will grow louder and louder until someone takes an action such as pulling down the mixer fader. If no action is taken, the howling will continue to grow in intensity until the gain is reduced by built-in compression or clipping. If there is no appropriate compression or loudspeaker protection, such runaway acoustic feedback is likely to result in loudspeaker damage.

Condition for Acoustic Feedback

As explained earlier, when the loop gain is at unity, the acoustic feedback is just sufficient to be self-sustaining. Therefore, the condition required for acoustic feedback to occur is when the loop gain is at or greater than unity or 0 dB.

This means that when the microphone hears just as “loud” from the loudspeaker as what was being initially input into the microphone, acoustic feedback is on the verge of occurring. To avoid acoustic feedback, the loop gain should be much less than unity, for example at -6 dB or less.

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